cp's OEIS Frontend

A136283 Number of graphs on n labeled nodes with degree at most 4.

%I A136283 #6 Aug 25 2017 23:38:13
%S A136283 1,2,8,64,1024,27449,1052793,53470067,3451287371,275322712826,
%T A136283 26566919914276,3047264283807562,409523561958024458,
%U A136283 63703577287372238069,11351386036074641226649,2296295762734645223170899,523223196906671550193022083,133357299601279100522308107142
%N A136283 Number of graphs on n labeled nodes with degree at most 4.
%D A136283 D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.
%H A136283 Andrew Howroyd, <a href="/A136283/b136283.txt">Table of n, a(n) for n = 1..50</a>
%o A136283 (PARI)
%o A136283 GraphsWithDegreeAtMost(n,limit)={
%o A136283 local(M=Map());
%o A136283 my(acc(p,v)=my(z); mapput(M, p, if(mapisdefined(M, p, &z), z+v, v)));
%o A136283 my(recurse(p,i,q,v,e)=if(e<=limit&&poldegree(q)<=limit, if(i<0, acc(x^e+q, v), my(t=polcoeff(p,i)); for(k=0, t, self()(p, i-1, (t-k+x*k)*x^i+q, binomial(t,k)*v, e+k)))));
%o A136283 my(iterate(v,k,f)=for(i=1,k,v=f(v));v);
%o A136283 vecsum(Vec(iterate(Mat([1,1]), n-1, src->M=Map(); for(i=1, matsize(src)[1], my(p=src[i,1]); recurse(p,poldegree(p),0,src[i,2],0)); Mat(M)))[2]); }
%o A136283 a(n) = GraphsWithDegreeAtMost(n, 4); \\ _Andrew Howroyd_, Aug 25 2017
%Y A136283 Cf. A000085 (degree at most 1), A136281-A136286.
%K A136283 nonn
%O A136283 1,2
%A A136283 _Don Knuth_, Mar 31 2008
%E A136283 Terms a(13) and beyond from _Andrew Howroyd_, Aug 25 2017